TY - JOUR
T1 - A Posteriori Error Control for Three Typical Force-Based Atomistic-to-Continuum Coupling Methods for an Atomistic Chain
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 233
EP - 264
PY - 2018
DA - 2018/09
SN - 12
DO - http://doi.org/10.4208/nmtma.OA-2017-0094
UR - https://global-sci.org/intro/article_detail/nmtma/12699.html
KW - 
AB - <p style="text-align: justify;">We consider the problem of a posteriori error estimates and adaptivity for three typical force-based atomistic-to-continuum coupling methods. Combining the residual and the stability estimates, we derive computable a posteriori error estimators for the three methods in the energy norm and formulate adaptive algorithms using these estimators. Our numerical experiments show optimal convergence rates of these algorithms. The efficiency of the estimators is also demonstrated numerically.</p>